|
|
A350295
|
|
2nd subdiagonal of the triangle A350292.
|
|
2
|
|
|
6, 8, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1431, 1485, 1540
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
3,1
|
|
LINKS
|
|
|
FORMULA
|
a(n) = binomial(n, 2) = A000217(n-1) for n > 4 with a(3) = 6 and a(4) = 8 (see Theorem 3 in Harborth and Nienborg).
O.g.f.: x^3*(2*x^4 - 3*x^3 - 4*x^2 + 10*x - 6)/(x - 1)^3.
E.g.f.: x^2*(x^2 + 6*x + 6*exp(x) - 6)/12.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 7.
|
|
MATHEMATICA
|
Join[{6, 8}, Table[Binomial[n, 2], {n, 5, 56}]]
LinearRecurrence[{3, -3, 1}, {6, 8, 10, 15, 21}, 60] (* Harvey P. Dale, Jul 01 2022 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|